Welcome! This is Crystallina, giving you a warm welcome to Jezzball State, an entire state solely dedicated to Jezzball.
But what is Jezzball? According to the Overview: "On a far-off world, a new kind of atom has been discovered. It's called a Jezz, and you get paid galactic credits each time you trap one for shipment back to Earth. The Jezz atoms preserve their energy best when tightly confined, so the smaller the chamber you trap them in, the more galactic credits you acquire. The game begins in a large capture chamber with two Jezz atoms bouncing around. With a click of the mouse, you can build a new chamber wall and trap the Jezz atoms in a smaller space. But be careful, if you don't build your wall completely across the chamber before it's hit by a Jezz atom, it won't withstand the impact. Be forewarned, JezzBall is not just challenging and great fun, but also strangely soothing and satisfying. Once you start trapping atoms, you won't want to stop!"

In other words, clear the grey space and don't let the Jezzballs collide with the walls which you are clearing. Sound simple? Try the later levels. You'll see how challenging this game can become.